Mathematics

Mathematics

Problem

At x=4x=4, the graph of a function gg shows an open circle at (4,5)(4,5), while the rest of the curve approaches y=5y=5 from both sides. A solid dot is placed at (4,7)(4,7). Answer the following: a. (i) Find lim⁡x→4−g(x)\displaystyle \lim_{x\to 4^-} g(x). (ii) Find lim⁡x→4+g(x)\displaystyle \lim_{x\to 4^+} g(x). (iii) State whether lim⁡x→4g(x)\displaystyle \lim_{x\to 4} g(x) exists. (iv) Is gg continuous at x=4x=4? Give reason.

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